Let $K$ be a number field and $I$ be an ideal in the ring of integers $\mathcal{O}_K$. Let $n$ be the smallest positive integer in $I \cap \mathbb{Z}$. I'm trying to figure out what to call $n$.

When $I$ is prime $n$ is the characteristic of the residue field. Is it appropriate to call $n$ the "characteristic of $I$" for general $I$, or is this a horrid abuse of terminology? Is there something else that's widely accepted?

EDIT: It looks like ``characteristic'' can be defined for any ring, so $n$ is the characteristic of $\mathcal{O}_K/I$. Perhaps it's not too much of a stretch to call it the characteristic of $I$??